The Cuban missile crisis happened back in October 1962, 50 years ago at around this time. I don't think any of us here were around at the time, so it's kind of hard for us to understand these days just how close we came to starting World War 3 because of it.
What I find remarkable about the Cuban missile crisis was how it was resolved peacefully with virtually no casualties. Hard compromises had to be made (the Soviets removed their missiles from Cuba, while the U.S. removed theirs from Turkey), but the leaders of the two superpowers (Kennedy of the United States, and Khrushchev of the Soviet Union) ultimately did the right thing.
I find myself agreeing with many historians that never before or since has humanity ever come so close to completely destroying itself.